ci.mean.diff: Confidence Interval for the Difference in Arithmetic Means

In misty: Miscellaneous Functions 'T. Yanagida'

Confidence Interval for the Difference in Arithmetic Means

Description

This function computes a confidence interval for the difference in arithmetic means in a one-sample, two-sample and paired-sample design with known or unknown population standard deviation or population variance for one or more variables, optionally by a grouping and/or split variable.

Usage

ci.mean.diff(x, ...)

## Default S3 method:
ci.mean.diff(x, y, mu = 0, sigma = NULL, sigma2 = NULL,
             var.equal = FALSE, paired = FALSE,
             alternative = c("two.sided", "less", "greater"),
             conf.level = 0.95, group = NULL, split = NULL, sort.var = FALSE,
             digits = 2, as.na = NULL, write = NULL, append = TRUE,
             check = TRUE, output = TRUE, ...)

## S3 method for class 'formula'
ci.mean.diff(formula, data, sigma = NULL, sigma2 = NULL,
             var.equal = FALSE, alternative = c("two.sided", "less", "greater"),
             conf.level = 0.95, group = NULL, split = NULL, sort.var = FALSE,
             na.omit = FALSE, digits = 2, as.na = NULL, write = NULL, append = TRUE,
             check = TRUE, output = TRUE, ...)

Arguments

x	a numeric vector of data values.
...	further arguments to be passed to or from methods.
y	a numeric vector of data values.
mu	a numeric value indicating the population mean under the null hypothesis. Note that the argument mu is only used when y = NULL.
sigma	a numeric vector indicating the population standard deviation(s) when computing confidence intervals for the difference in arithmetic means with known standard deviation(s). In case of independent samples, equal standard deviations are assumed when specifying one value for the argument sigma; when specifying two values for the argument sigma, unequal standard deviations are assumed. Note that either argument sigma or argument sigma2 is specified and it is only possible to specify one value (i.e., equal variance assumption) or two values (i.e., unequal variance assumption) for the argument sigma even though multiple variables are specified in x.
sigma2	a numeric vector indicating the population variance(s) when computing confidence intervals for the difference in arithmetic means with known variance(s). In case of independent samples, equal variances are assumed when specifying one value for the argument sigma2; when specifying two values for the argument sigma, unequal variances are assumed. Note that either argument sigma or argument sigma2 is specified and it is only possible to specify one value (i.e., equal variance assumption) or two values (i.e., unequal variance assumption) for the argument sigma even though multiple variables are specified in x.
var.equal	logical: if TRUE, the population variance in the independent samples are assumed to be equal.
paired	logical: if TRUE, confidence interval for the difference of arithmetic means in paired samples is computed.
alternative	a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less".
conf.level	a numeric value between 0 and 1 indicating the confidence level of the interval.
group	a numeric vector, character vector or factor as grouping variable. Note that a grouping variable can only be used when computing confidence intervals with unknown population standard deviation and population variance.
split	a numeric vector, character vector or factor as split variable. Note that a split variable can only be used when computing confidence intervals with unknown population
sort.var	logical: if TRUE, output table is sorted by variables when specifying group.
digits	an integer value indicating the number of decimal places to be used.
as.na	a numeric vector indicating user-defined missing values, i.e. these values are converted to NA before conducting the analysis. Note that as.na() function is only applied to x, but not to group or split.
write	a character string naming a text file with file extension ".txt" (e.g., "Output.txt") for writing the output into a text file.
append	logical: if TRUE (default), output will be appended to an existing text file with extension .txt specified in write, if FALSE existing text file will be overwritten.
check	logical: if TRUE (default), argument specification is checked.
output	logical: if TRUE (default), output is shown on the console.
formula	a formula of the form y ~ group for one outcome variable or cbind(y1, y2, y3) ~ group for more than one outcome variable where y is a numeric variable giving the data values and group a numeric variable, character variable or factor with two values or factor levels giving the corresponding groups.
data	a matrix or data frame containing the variables in the formula formula.
na.omit	logical: if TRUE, incomplete cases are removed before conducting the analysis (i.e., listwise deletion) when specifying more than one outcome variable.

Value

Returns an object of class misty.object, which is a list with following entries:

call	function call
type	type of analysis
data	list with the input specified in x, group, and split
args	specification of function arguments
result	result table

Author(s)

Takuya Yanagida [e-mail]

References

Rasch, D., Kubinger, K. D., & Yanagida, T. (2011). Statistics in psychology - Using R and SPSS. John Wiley & Sons.

See Also

test.z, test.t, ci.mean, ci.median, ci.prop, ci.var, ci.sd, descript

Examples

dat1 <- data.frame(group1 = c(1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2,
                              1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2),
                   group2 = c(1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2,
                              1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2),
                   group3 = c(1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2,
                              1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2),
                   x1 = c(3, 1, 4, 2, 5, 3, 2, 3, 6, 4, 3, NA, 5, 3,
                          3, 2, 6, 3, 1, 4, 3, 5, 6, 7, 4, 3, 6, 4),
                   x2 = c(4, NA, 3, 6, 3, 7, 2, 7, 3, 3, 3, 1, 3, 6,
                          3, 5, 2, 6, 8, 3, 4, 5, 2, 1, 3, 1, 2, NA),
                   x3 = c(7, 8, 5, 6, 4, 2, 8, 3, 6, 1, 2, 5, 8, 6,
                          2, 5, 3, 1, 6, 4, 5, 5, 3, 6, 3, 2, 2, 4))

#-------------------------------------------------------------------------------
# One-sample design

# Example 1: Two-Sided 95% CI for x1
# population mean = 3
ci.mean.diff(dat1$x1, mu = 3)

#-------------------------------------------------------------------------------
# Two-sample design

# Example 2: Two-Sided 95% CI for y1 by group1
# unknown population variances, unequal variance assumption
ci.mean.diff(x1 ~ group1, data = dat1)

# Example 3: Two-Sided 95% CI for y1 by group1
# unknown population variances, equal variance assumption
ci.mean.diff(x1 ~ group1, data = dat1, var.equal = TRUE)

# Example 4: Two-Sided 95% CI with known standard deviations for x1 by group1
# known population standard deviations, equal standard deviation assumption
ci.mean.diff(x1 ~ group1, data = dat1, sigma = 1.2)

# Example 5: Two-Sided 95% CI with known standard deviations for x1 by group1
# known population standard deviations, unequal standard deviation assumption
ci.mean.diff(x1 ~ group1, data = dat1, sigma = c(1.5, 1.2))

# Example 6: Two-Sided 95% CI with known variance for x1 by group1
# known population variances, equal variance assumption
ci.mean.diff(x1 ~ group1, data = dat1, sigma2 = 1.44)

# Example 7: Two-Sided 95% CI with known variance for x1 by group1
# known population variances, unequal variance assumption
ci.mean.diff(x1 ~ group1, data = dat1, sigma2 = c(2.25, 1.44))

# Example 8: One-Sided 95% CI for y1 by group1
# unknown population variances, unequal variance assumption
ci.mean.diff(x1 ~ group1, data = dat1, alternative = "less")

# Example 9: Two-Sided 99% CI for y1 by group1
# unknown population variances, unequal variance assumption
ci.mean.diff(x1 ~ group1, data = dat1, conf.level = 0.99)

# Example 10: Two-Sided 95% CI for y1 by group1
# unknown population variances, unequal variance assumption
# print results with 3 digits
ci.mean.diff(x1 ~ group1, data = dat1, digits = 3)

# Example 11: Two-Sided 95% CI for y1 by group1
# unknown population variances, unequal variance assumption
# convert value 4 to NA
ci.mean.diff(x1 ~ group1, data = dat1, as.na = 4)

# Example 12: Two-Sided 95% CI for y1, y2, and y3 by group1
# unknown population variances, unequal variance assumption
ci.mean.diff(cbind(x1, x2, x3) ~ group1, data = dat1)

# Example 13: Two-Sided 95% CI for y1, y2, and y3 by group1
# unknown population variances, unequal variance assumption,
# listwise deletion for missing data
ci.mean.diff(cbind(x1, x2, x3) ~ group1, data = dat1, na.omit = TRUE)

# Example 14: Two-Sided 95% CI for y1, y2, and y3 by group1
# unknown population variances, unequal variance assumption,
# analysis by group2 separately
ci.mean.diff(cbind(x1, x2, x3) ~ group1, data = dat1, group = dat1$group2)

# Example 15: Two-Sided 95% CI for y1, y2, and y3 by group1
# unknown population variances, unequal variance assumption,
# analysis by group2 separately, sort by variables
ci.mean.diff(cbind(x1, x2, x3) ~ group1, data = dat1, group = dat1$group2,
             sort.var = TRUE)# Check if input 'y' is NULL

# Example 16: Two-Sided 95% CI for y1, y2, and y3 by group1
# unknown population variances, unequal variance assumption,
# split analysis by group2
ci.mean.diff(cbind(x1, x2, x3) ~ group1, data = dat1, split = dat1$group2)

# Example 17: Two-Sided 95% CI for y1, y2, and y3 by group1
# unknown population variances, unequal variance assumption,
# analysis by group2 separately, split analysis by group3
ci.mean.diff(cbind(x1, x2, x3) ~ group1, data = dat1,
             group = dat1$group2, split = dat1$group3)

#-----------------

group1 <- c(3, 1, 4, 2, 5, 3, 6, 7)
group2 <- c(5, 2, 4, 3, 1)

# Example 18: Two-Sided 95% CI for the mean difference between group1 and group2
# unknown population variances, unequal variance assumption
ci.mean.diff(group1, group2)

# Example 19: Two-Sided 95% CI for the mean difference between group1 and group2
# unknown population variances, equal variance assumption
ci.mean.diff(group1, group2, var.equal = TRUE)

#-------------------------------------------------------------------------------
# Paired-sample design

dat2 <- data.frame(pre = c(1, 3, 2, 5, 7, 6),
                   post = c(2, 2, 1, 6, 8, 9),
                   group = c(1, 1, 1, 2, 2, 2), stringsAsFactors = FALSE)

# Example 20: Two-Sided 95% CI for the mean difference in pre and post
# unknown poulation variance of difference scores
ci.mean.diff(dat2$pre, dat2$post, paired = TRUE)

# Example 21: Two-Sided 95% CI for the mean difference in pre and post
# unknown poulation variance of difference scores
# analysis by group separately
ci.mean.diff(dat2$pre, dat2$post, paired = TRUE, group = dat2$group)

# Example 22: Two-Sided 95% CI for the mean difference in pre and post
# unknown poulation variance of difference scores
# analysis by group separately
ci.mean.diff(dat2$pre, dat2$post, paired = TRUE, split = dat2$group)

# Example 23: Two-Sided 95% CI for the mean difference in pre and post
# known population standard deviation of difference scores
ci.mean.diff(dat2$pre, dat2$post, sigma = 2, paired = TRUE)

# Example 24: Two-Sided 95% CI for the mean difference in pre and post
# known population variance of difference scores
ci.mean.diff(dat2$pre, dat2$post, sigma2 = 4, paired = TRUE)

# Example 25: One-Sided 95% CI for the mean difference in pre and post
# unknown poulation variance of difference scores
ci.mean.diff(dat2$pre, dat2$post, alternative = "less", paired = TRUE)

# Example 26: Two-Sided 99% CI for the mean difference in pre and post
# unknown poulation variance of difference scores
ci.mean.diff(dat2$pre, dat2$post, conf.level = 0.99, paired = TRUE)

# Example 27: Two-Sided 95% CI for for the mean difference in pre and post
# unknown poulation variance of difference scores
# print results with 3 digits
ci.mean.diff(dat2$pre, dat2$post, paired = TRUE, digits = 3)

# Example 28: Two-Sided 95% CI for for the mean difference in pre and post
# unknown poulation variance of difference scores
# convert value 1 to NA
ci.mean.diff(dat2$pre, dat2$post, as.na = 1, paired = TRUE)

misty documentation built on June 29, 2024, 9:07 a.m.